Discovery or Direction? Active learning strategies in secondary mathematics and the implications for curriculum reform in Northern Ireland by Miss Erin Dawson

Degree Programme: PGCE (Mathematics)

Introduction

Under the United Nations, every child has the right not only to education (United Nations, 1989), but also to an education which provides them with life skills, allowing them to develop “to their fullest potential” (UNCRC, 2001, p.1). A core element of any child’s education is mathematics, as through learning mathematics learners are provided with valuable life skills such as budgeting, reading timetables, and problem-solving skills.

In Northern Ireland, the Department of Education has announced the TransformED strategy. Designed for implementation starting in 2028, the strategy calls for “up-to-date, evidence-informed practice […] shaped by research on what really works” (Department of Education (DENI), 2025, p. 10). As such, it is vital that educational practices and pedagogies, such as active learning, be researched, to consider both their benefits and limitations, to ensure that any evidence-informed practice which results from the TransformED strategy is to the benefit of Northen Irish school pupils.

Although the term “active learning” is widely used in both educational literature and educational policy discourse, it is somewhat difficult to define. There is a lack of consensus on the definition, resulting in interpretation often left to the reader. In the literature, some suggested definitions differ significantly from others. For example, some posit that active learning simply involves pupils being engaged in the learning process (University of Minnesota, n.d.), while Clark, et al. (2012) suggest that active learning involves teachers becoming facilitators of education rather than educators in their own right. This suggests that, through active learning, pupils “discover or construct some or all of the essential information for themselves” (Clark, et al., 2012, p. 6).

The Council for the Curriculum, Examinations and Assessment (CCEA) advocate for active learning techniques to be adopted throughout classrooms in Northern Ireland. CCEA indicates that active learning occurs when social collaboration takes place within the classroom (CCEA, 2007). In this essay, the benefits and limitations of active learning will be discussed, with reference to both literature and experience. This discussion will then inform a conclusion, suggesting a learning approach to maximise the overall benefit that pupils derive from their educational experiences.

The case for active learning

Vygotsky (1978) argued that “social experience” plays a “dominant role” in human development (p. 22). By adopting a similar lens, Sfard (2011) posits that, through social learning experiences, learners can transition from simply acquiring knowledge to participating in a community, which, at its core, entails “the ability to communicate” (p. 6). Clearly, then, given the social definition ascribed to active learning in Northern Ireland, there is an argument for active pedagogy in mathematics classrooms.

In advocating for active learning, CCEA argues that today’s society requires an education that encourages skills such as problem-solving, decision-making, critical thinking, and the ability to work effectively in a group (CCEA, 2007). CCEA posit that these skills require more than knowledge, and can best be cultivated through learning, which, they suggest, will make education a “more relevant, enjoyable and motivational experience” through which pupils will “come to a deeper understanding” (pp. 1-2)

Engagement or Exhaustion?

In researching the impact of collaborative pedagogical strategies in mathematics, Cantley et al. (2017) found that these strategies can improve “interest and enjoyment of mathematics” (p. 23), especially for girls. It is also noteworthy that scholars such as Fuster-Guilló, et al. (2019) have found a positive correlation between motivation and academic achievement, with pupils who experience improved motivation also showing “improved academic performance” (Fuster-Guilló et al., 2019, p. 7), and with enhanced motivation “translated into an increase in test scores” (O’Neil et al., 1995, p. 154).

However, despite the potential of active learning to increase interest and motivation, Swan (2005) and Drew & Mackie (2011) have argued that it may be more challenging to implement than direct instruction. Swan (2005) posits that the introduction of active learning, especially to pupils who have not experienced it before, may lead to confusion and challenges for the teacher – “[some pupils] appeared confused and challenged their teacher to explain why they were expected to learn in these new ways” (p. 30). Drew & Mackie (2011) also argued that active learning may be “problematic for teachers since it appears to position them in more of a sidelined teaching role” (p. 13).

Both improved interest and motivation, alongside the difficulty of implementation, were evident throughout my first teaching placement. I noticed that collaborative, active learning could have a significant impact on motivation and achievement during a lesson in which pupils worked in teams to answer numeracy-based questions and consider strategies to maximise their points (Appendix 1 for the lesson plan). I concluded after this lesson that the game appeared to “work very well” as “pupils were engaged throughout”. Further, I noted that the numeracy questions, which had posed a problem for this class in their winter assessment, no longer appeared to be an issue, providing some evidence that an active approach can improve both motivation and achievement to some extent, as argued by Fuster-Guilló et al. (2019). 

However, the suggestion that active learning may be difficult to implement in some situations resonates closely with my experience. Implementing active learning in the number line walks lesson (Appendix 3) proved challenging, which may have compromised pupils’ ability to develop a deeper understanding of the topic. In the end-of-topic homework, fewer than 30% of the class were able to correctly answer the question 14 – (-8), indicating that a deep understanding of the topic had not been acquired, despite the use of active learning approaches. Active learning, discussion, and the use of manipulatives such as algebra tiles were also employed to teach algebraic multiplication to a low-attaining Year 11 class (Appendix 4 for the lesson plan). In my evaluation of the lesson, I noted that the pupils, having never encountered these resources or experienced this type of lesson before, appeared disinterested and “answered better when given a rule”, thus supporting the argument that active learning may lead to confusion, which consequently poses practical challenges in its implementation (Chall, 2000; Kirshner et al., 2006; O’Neil, 1995).

These mixed findings are particularly pertinent within the context of TransformED (Department of Education (DENI), 2025). Whilst the promise of active learning within mathematics is clear through the improved engagement which has been evidenced, there are clear implementation challenges which suggest that curriculum reform in this area must be accompanied by teacher preparation and support.

Problem solving or Confusion?

Problem solving skills refer to the skills required for pupils to answer problem style questions, where they “do not have well-rehearsed, ready-made methods” (EEF, 2017, p. 14). Drew and Mackie (2011) posit that “active learning strategies such as social interaction” (p. 459) are relevant in fostering “effective learning […] and problem solving” (Drew & Mackie, 2011, p. 459, citing Dennick, 2008). The positive impact that active learning may have on problem solving skills is further supported by Burns et al. (2014), with the authors arguing that, through active learning, pupils learn to “construct knowledge in different ways” (p. 19), thus benefiting higher-level analysis of questions and problem-solving skills.

Despite this, the literature suggests that active learning strategies, which allow pupils to learn through discovery, can leave pupils “lost and frustrated”, with this confusion leading to the acquisition of misconceptions (Kirschner et al., 2006, citing Brown & Campione, 1994). This is supported, for example, by Chall (2000), who argued that while attitudes towards learning may be slightly improved with a more progressive (active) approach, accuracy of knowledge and overall academic performance appear to benefit to a greater extent from direct instruction approaches, “traditional classes came out considerably higher in achievement” (p. 171).

Again, the findings from the literature that active learning can improve pupils’ problem-solving skills but can also create confusion were reflected in my own teaching experiences. I witnessed the impact of active learning on problem solving skills through an investigation pertaining to the properties of cylinders, which required pupils to work in pairs to answer some problem-style questions based on previously taught material (Appendix 2 for lesson plan). In my lesson evaluation, I noted that “Interesting discussions were had, and pupils were genuinely engaged in trying to get these questions correct”. Because of the opportunity to work with their peers to consider ideas, more pupils appeared to be able to access the problem-style questions than if they had been asked to attempt the questions individually, thereby demonstrating their ability to “construct knowledge in different ways”, as suggested by Burns et al. (2014, p. 19).  However, for older classes, the introduction of a new active pedagogy was seen as causing confusion, as evidenced by my lesson with Year 11 (Appendix 4). I noted in my reflection that when pupils were asked to complete some independent practice, only a small minority chose to use active learning strategies to help them. The apparent confusion surrounding the active learning strategies resonates with the findings of Kirschner et al. (2006), as encouraging pupils to discover a rule for algebraic multiplication independently and actively led to confusion and frustration.

These findings support those in the wider literature. Whilst collaborative and active learning enhanced problem-solving abilities for some pupils (Appendix 2), the confusion observed among older pupils (Appendix 4) suggests that familiarity with traditional approaches may mediate their effectiveness.

Understanding or Overload?

“When you really understand something, you never forget it” (Swan, 2005, p. 30). In challenging pedagogical approaches which require pupils to watch, listen and imitate a skill until they are fluent, Swan (2005) suggests that “a collaborative activity in which learners are challenged to arrive at understanding through discussion” (p. 5) may be more effective. The collaborative, discursive nature of this proposed activity style resonates with CCEA’s construal of active learning, suggesting that deeper levels of understanding may be reached through it. The finding that collaborative, active learning improved understanding is echoed by Burns, et al. (2014), who argued that, through group processing, “team members help one another understand” (p. 20).

However, Kirshner et al. (2006) argue that novice learners require guidance through direct instruction style teaching, which they define as “providing information that fully explains the concepts and procedures that students are required to learn” (p. 75). By striking a balance between direct instruction and active learning, Rosenshine (2012) emphasises that appropriate consideration should be given to the order in which different pedagogical approaches are used – “students need extensive, successful, independent practice in order for skills and knowledge to become automatic” (p. 18). Rosenshine noted that “the most effective teachers” (p. 12) provide learning experiences through direct instruction, and that where these teachers choose to utilise active learning strategies, “they always did the experiential activities after, not before, the basic material was learned” (p. 12). Therefore, while the benefits of active learning strategies are often reaped by teachers, these strategies may be more effective for consolidating knowledge than for teaching new content.

Throughout the teaching placement, I observed some pupils gaining understanding of topics through active learning techniques, such as through the use of number line walks for integer arithmetic (Appendix 3), and through the improved problem-solving skills discussed previously (Appendix 2), in keeping with what literature suggests around active learning (Burns et al., 2014; Swan, 2005). Whilst in some cases further work was needed to consolidate these topics, active learning pedagogies provided an engaging introduction and helped pupils achieve some success.

However, and to some extent consistent with Rosenshine’s emphasis on the importance of appropriate sequencing of activities within the learning experience (Rosenshine, 2012), I found that active learning was less confusing to pupils when used towards the end of a topic. This is supported by a comparison of my own experience with the Year 11 lesson (Appendix 4) with a lesson I taught to a Year 9 class at the end of a topic (Appendix 5 for lesson plan). In the active lesson with Year 9, which took place at the end of the topic of expanding algebraic brackets, I noted that “pupils engaged with the scavenger hunt well – in fact they seemed excited about the idea of it”. This is in stark contrast to the evaluation of the active learning lesson presented in Appendix 4. Unlike the lesson presented in Appendix 4, the topic was initially introduced to pupils using direct instruction before allowing them to further develop their skills using active learning. I noticed a significant improvement in pupils’ engagement and a concomitant reduction in their confusion during the Year 9 lesson, compared with what I observed in Year 11.

These findings suggest that the effectiveness of active learning in mathematics is not simply a question of whether such strategies are employed, but crucially, of where within the instructional sequence they are positioned.

Conclusion

In this essay, several benefits and limitations of active learning have been discussed, drawing on perspectives from the literature and my own professional experience during my first teaching placement. Arguments in favour of active learning include its positive impact on motivation (Cantley et al., 2017) and the potential this creates for increased attainment (Fuster-Guilló et al., 2019; O’Neil et al., 1995), the fostering of problem-solving skills (Burns et al., 2014; Drew & Mackie, 2011), and the potential for developing deeper levels of understanding (Burns et al., 2014; Swan, 2005). However, potential limitations of active learning, such as its potential to lead to confusion (Chall, 2000; Kirshner et al., 2006), difficulty in its implementation (Drew & Mackie, 2011), and the necessity of appropriate sequencing of pedagogical approaches (Rosenshine, 2012), render it problematic to argue that active learning should become the default teaching strategy. 

During my first teaching placement, I experienced both advantages and disadvantages associated with active learning. This has led me to conclude that active learning plays an important role in mathematical pedagogy, but as an augmentation rather than a replacement for direct instruction. Such an approach would help to ensure that pupils are equipped with mathematical knowledge in a way that not only motivates and engages but also mitigates against confusion. By adopting the form of pedagogy advocated by Rosenshine (2012), teachers may harness the benefits of both active learning strategies and direct instruction approaches, providing due consideration is given to the order in which these are utilised to optimise their overall benefit to pupils’ mathematical learning.

Within the context of TransformED (Department of Education (DENI), 2025), these findings serve as both an endorsement of active learning and a caution. Whilst the reforms emphasise strategies that enhance motivation and problem-solving, potentially including active learning within these approaches, the observed limitations suggest that these ambitions will only be realised after considering the suitability and sequencing of such approaches.

References

Burns, M., Pierson, E. & Reddy, S., 2014. Working Together: How Techers Teach and Students Learn in Collaborative Learning Environments. International Journal of Instruction, 7(1), pp. 17-32.

Cantley, I., Prendergast, M. & Schlindwein, F., 2017. Collaborative cognitive-activation strategies as an emancipatory force in promoting girls’ interest in and enjoyment of mathematics: a cross-national case study. International Journal of Educational Research, 81(1), pp. 38-51.

CCEA, 2007. Active Learning and Teaching Methods for Key Stage 3, Belfast: CCEA.

Chall, J. S., 2000. The Academic Achievement Challenge: What Really Works in the Classroom? 1st ed. New York: The Guildford Press.

Clark, R. E., Kirshner, P. A. & Sweller, J., 2012. Putting students on the path to learning: The case for fully guided instruction. American Educator, 36(1), pp. 6-11.

Drew, V. & Mackie, L., 2011. Extending the constructs of active learning: implications for teachers’ pedagogy and practice. Curriculum Journal, 22(4), pp. 451-467.

EEF, 2017. Improving mathematics in key stages two and three: Guidance report, London: Education Endowment Fund.

Fuster-Guilló, A. et al., 2019. Evaluating Impact on Motivation and Academic Performance of a Game-Based Learning Experience Using Kahoor. Frontiers in Psychology, 10(1), pp. 1-8.

Kirshner, P. A., Sweller, J. & Clark, R. E., 2006. Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 21(2), pp. 75-86.

O’Neil, H. F., Sugrue, B. & Baker, E. L., 1995. Effects of Motivational Interventions on the National Assessment of Educational Progress Mathematics Performance. Educational Assessment, 3(2), pp. 135-157.

Rosenshine, B., 2012. Principles of Instruction: Research – Based Strategies That All Teachers Should Know. American Educator, 36(1), pp. 12-39.

Sfard, A., 1998. On Two Metaphors for Learning and the Danger of Choosing Just One. Educational Researcher, 27(2), pp. 4-13.

Swan, M., 2005. Improving learning in mathematics: Challenges and strategies, London: Department for Education and Skills.

University of Minnesota, n.d. Active Learning. Available at: https://cei.umn.edu/teaching-resources/active-learning

Vygotsky, L. S., 1978. Mind in Society. 1st ed. Cambridge, MA: Harvard University Press.